Electrical machines in general are constructed from laminations of electrical sheet steel, the resulting structure being used to carry the magnetic flux on which the machine depends for its operation. The structure is laminated to reduce the effect of eddy currents, which flow in the steel due to the time rate of change of the flux. Usually only machines with unvarying flux have unlaminated structures. For example, the field structure of a dc machine can be unlaminated (i.e. made of solid metal), though even in these machines a laminated structure is often adopted in order to reduce the transient response when the machine is subjected to a new operating condition. The degree of lamination is usually based on the frequency of flux variation in the machine. For example, in a machine energised directly from the 50 or 60 Hz mains supply and operating at, say, 1500 or 1800 rev/min, a lamination thickness of 0.50 or 0.65 mm is often adopted. For a machine operating on a 400 Hz supply and running at 12000 rev/min, a lamination thickness of 0.20 mm might be selected.
The laminations are stacked to provide a pack or core of the desired length. Stationary laminations form the stator core and are typically inserted in a frame or provided with some other structure to secure it against the torque reaction experienced during operation. Moving laminations form the rotor core and are typically mounted on a shaft which is housed in a bearing system.
One example of an electrical machine which uses this arrangement is the switched reluctance machine. A general treatment of electrical drives which incorporate switched reluctance machines can be found in various textbooks, e.g. “Electronic Control of Switched Reluctance Machines” by T J E Miller, Newnes, 2001, incorporated herein by reference. More detail is provided in the paper “The characteristics, design and application of switched reluctance motors and drives” by Stephenson and Blake, PCIM'93, Nürnberg, 21-24 Jun. 1993, incorporated herein by reference.
FIG. 1 shows typical rotor and stator laminations for a switched reluctance machine. Both laminations have salient poles and some or all of the stator poles carry coils which are interconnected to form one or more phase windings. In the example shown, the rotor lamination 16 has four poles 14, the stator lamination 10 has six poles 11 with six coils 13 connected in opposite pairs to form three phase windings, A, B & C. The rotor laminations are mounted on a shaft 18. As is well known in the art, the number of stator and rotor poles, the number of coils and the number of phase windings can vary widely and are selected by the designer to suit the criteria of the design in hand.
The salient poles of the rotor lamination extend radially outward from a core portion of the rotor lamination. The core portion comprises a cut-out for accommodating the shaft 18. A root portion of the salient pole is adjacent to the core portion. An outer contour or profile of the lamination defines: a fillet radius at the root portion, smoothly joining the salient pole to the core portion; a pole face at a radially outer aspect of the salient pole; and, typically, straight sides between the pole face and the fillet radii on each side of the salient pole. Typically, a centre line of the salient pole coincides with a radius through the axis of rotation.
Typically, the rotor does not carry any windings, so the rotor assembly is generally much more robust than for other types of machine which have windings or magnets mounted on the rotor. While this characteristic enables operation of the rotor at higher speeds than would normally be contemplated by designers, there are applications which still demand ever higher speeds, e.g., drives for flywheels, turbines and material testing equipment.
The limit on the useful speed of the rotor of a switched reluctance motor is typically the stress induced in the lamination by the centrifugal forces. While the elastic stress limit of lamination steel varies a little from one grade of steel to another, a typical yield stress is in the region of 350 MPa, so the designer would probably design for a peak of around 280 MPa to allow a suitable safety margin.
FIG. 2 shows the results of a stress analysis for a rotor lamination having 8 rotor poles. This analysis is performed by setting up a finite element model of a sector of the lamination and solving for the centrifugal stresses. This particular lamination has an inside (shaft) diameter of 145 mm and a mass of 376 kg per meter of stack length. Stress contours at 10,000 rev/min are shown in FIG. 2 in MPa (e.g., contours along which the stress at 10,000 rev/min is approximately equal to 45 MPa, 90 MPa, 135 MPa, and 180 MPa). The analysis shows that the highest stress region is around the shaft with a stress of around 180 MPa. This would indicate that the material is not being used to its full capabilities and that the rotor mass could be reduced.
One known method of achieving these objects is to increase the shaft diameter and make it hollow. FIG. 3 shows the lamination of FIG. 2 modified in this way, with the shaft diameter increased from 145 mm to 197 mm. This reduces the mass of the lamination and, although using a solid shaft would simply maintain the overall mass at around the same level, the use of a hollow shaft yields a net reduction in the mass of the assembly. FIG. 3 shows that the shaft diameter has been increased to such a degree that the peak stress in the rotor lamination at 10,000 rev/min is now at its maximum design level, i.e., around 270 MPa (see, e.g., the stress contours in FIG. 3 along which the stress at 10,000 rev/min is approximately equal to 45 MPa, 90 MPa, 135 MPa, 180 MPa, 225 MPa, and 270 MPa). The limiting areas are two regions at the root of the pole. According to the known method, this represents the maximum shaft diameter that can be used.
Further increases of the shaft diameter, while reducing the mass of the laminations, would bring unacceptable increases in peak stress at the pole root, as shown in FIG. 4, where the shaft diameter has been increased to 210 mm. In FIG. 4, the values of the contour lines in the pole body are as in FIG. 3, but the stress at the root of the poles is now above 300 MPa at 10,000 rev/min, which is not acceptable for a safe design (see, e.g., the stress contours in FIG. 4 along which the stress at 10,000 rev/min is approximately equal to 225 MPa, 270 MPa, and 315 MPa).
U.S. Pat. No. 3,956,678 discloses an electrical machine having salient poles with holes near the pole face to provide a non-symmetric saturation-dependent flux pattern. A hybrid switched reluctance and permanent magnet motor having a circumferential, slot-shaped hole near the pole face for the same purpose is disclosed in “A new Low-Cost Hybrid Switched Reluctance Motor for Adjustable Speed Pump Applications”, K. Y. Lu et al, Proceedings of 41st Annual Meeting of the Industrial Applications Society, Tampa, Fla., 08-12 Oct. 2006. In their position close to the pole face, these holes do not affect the peak stress in or near the root portion of the salient pole.
A switched reluctance motor having a rectangular window near the root portion of a salient rotor pole for the purpose of acoustic noise reduction is disclosed in “Novel Rotor Pole Design of Switched Reluctance Motors to Reduce the Acoustic Noise”, M. Sanada et al, IAS2000, Thirty-fifth Annual Meeting and World Conference on Industrial Applications of Electrical Energy, 08-12 Oct. 2000, Rome, Italy, Vol 1, pp 107-113. The sharp corners of the rectangular hole in the peak stress region near or at the root portion of the pole act to increase, rather than to decrease, peak stress in the rotor.
There is therefore a need for a design for a salient pole rotor lamination which keeps within the design peak stress level for the lamination, while substantially maintaining the quality of the electromagnetic performance of the machine.